Question

if 3x + 4y = 16 and xy = 4 ; find the value of 9x^2 + 16y^2 .

Answer 1

3x^2=9x^2;4y^2=16^2
so,9x^2+16y^2 can be written as (3x+4y)^2
(a+b)=a^2+2ab+b^2
where a=3x,b=4y
$({3x})^{2} + 2 (3x )(4 y) + ({4y})^{2}$
then,9x^2+24(xy=4)+16y^2
$9 {x}^{2} + 96 + 16 {y}^{2}$